Abstract

The standard win-stay, lose-shift behavior strategy in the repeated Prisoner's Dilemma game prescribe the players that win and lose in a current game round to keep and to change, respectively, their current actions, in the next round. Winning and losing are understood as receiving one of two upper values and one of two lower values, respectively, among the four admissible values for the players' benefits. In particular, a player acting as a cooperator against coperation wins and therefore is not allowed to switch to defection in the next round with a hope to gain more (provided his/her rival keeps cooperating). This constraint can be viewed as too strong for a selfish player. Here, we discuss a two-step win-stay, lose-shift behavior that differs from the traditional win-stay lose-shift one in understanding of winning and losing. A player wins if his/her benefit is no smaller that in the previous round, and loses otherwise. This pattern is in a sense more selfish; in particular, a switch from cooperation (against cooperation) to defection is not forbidden. Another confirmation of a more selfish character of the two-step win-stay, lose-shift behavior, compared to the standard win-stay, lose-shift one, is that the former does not bring two individuals playing the repeated Prisoner's Dilemma game to mutual cooperation. In this paper, our goal is to understand to what degree one can relax the two-step win-stay, lose-shift behavior in selfishness so as to reach mutual cooperation, anyway. We deal with two models of the repeated Prisoner's Dilemma game - a game of two individuals and a game in a group of players. In the game of two individuals, a relaxed two-step win-stay, lose-shift behavior assumes that the players use mixed straegies; here, relaxation is associated with patience. In the game in a group of players, relaxation is achieved through conformity, a tendency to join the majority. We show that even a small degree of conformity is enough to teach a two-step win-stay, lose-shift group to cooperate.